Re: 0^0 equals 1 or undefined?

Yes. I see nothing wrong with that equality even if x=0. It's the stepx^(1-1) = x^1 * x^(-1) that I have trouble with when x=0. It appears to be applying the law of exponents x^(a+b) = x^a * x^b. When x=0 and b=-1 the second factor is 0^(-1) which is what I have trouble with. To me this is indicating the reciprocal of 0 (equivalent notationally to 1/0) which the multiplicative inverse axiom precludes.

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

Re: 0^0 equals 1 or undefined?

Yes, it is applying that identity, which should be true for all x,a and b. But because this leads to division by zero, we rather leave 0^0 as undefined.

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: 0^0 equals 1 or undefined?

Yes. I agree that x^0 = x^(1-1) even if x=0. It's the x^(1-1) = x^1 * x^(-1) I have trouble with.It appears to me that this is an application of the exponent rule x^(n+m) = x^n * x^m. But when x=0 the right hand side has the factor 0^(-1) which to me indicates the reciprocal of zero which does not exist. So it seems a law of exponents is being applied to an expression that has in it an undefined quantity. That appears to me to be an invalid step.

Oops! I thought post #26 got lost in hyperspace, so I redid it as #28.

Last edited by noelevans (2012-07-22 12:08:43)

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

Re: 0^0 equals 1 or undefined?

It leads to an undetermined expression for x=0 so that means the starting expression is also undetermined for x=0.

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: 0^0 equals 1 or undefined?

0/0 is symbolism in calculus for an indeterminate form, not for a number in the Reals.Since 0 has no multiplicative inverse 0/0 which would come from the definition of division and the product of 0 with its reciprocal is NOT an ALLOWABLE construct in the field; that is, we shouldn't even be writing it and viewing it as if it might be a real number.

Also when defining fractions starting with the whole numbers W={0,1,2,3,...} they are typically defined by the set F = { p/q | p and q are whole numbers and q is not zero }. There is no member of this set F that has a zero in the denominator. To write 2/0 for example is to write something that is not a fraction.

But 0^0 as argued earlier is not equivalent to 0/0. We are not then constrained to leave it out of our definition. We can leave it out of our definition of exponentiation or make our defininition ofexponentiation include it. If left out of the definition it remains undefined. If we include it in our definition then one would hope that it would make sense. Defining ... x^3=1*x*x*x, x^2=1*x*x , x^1=1*x and following this "pattern" sensibly produces x^0 = 1 (multiplied by no x's).

I like 0^0 = 1 because as stated several times already it sure is CONVENIENT. One convenience not mentioned before is that for expressions in algebra like (2x-1)^0, this equals 1 when x=1/2. So we don't have to make an exception and say that (2x-1)^0 =1 EXCEPT when x=1/2.

Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional).LaTex is like painting on many strips of paper and then stacking them to see what picture they make.

Re: 0^0 equals 1 or undefined?

My argument from the other topic, Don Blazys', applies here, too. If we remove the removable singularity, we won't get the same function.

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: 0^0 equals 1 or undefined?

There is no reason to put that into hide tags...

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: 0^0 equals 1 or undefined?

Who says so?

Did you watch that video I just posted?

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: 0^0 equals 1 or undefined?

Hm, okay then. But what are the privileges of defining 0.999... to "exist" as a mathematical concept and be equal to 1?

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: 0^0 equals 1 or undefined?

Like what?

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: 0^0 equals 1 or undefined?

Last edited by anonimnystefy (2013-02-06 22:14:13)

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: 0^0 equals 1 or undefined?

No, the 0^0 is okay.

0.999... isn't. Making 0.999... barred from mathematics makes as much sense as making it equal to 1

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.

Re: 0^0 equals 1 or undefined?

No, that sum is 1.

Here lies the reader who will never open this book. He is forever dead.Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and PunishmentThe knowledge of some things as a function of age is a delta function.